The authors blend the three sources of inspiration. Firstly, they
contemplate the ``one-dimensional" (i.e.,  ordinary, first-order,
two-component) Dirac eq. (2.3) of ref. [52] and eliminate one of the
components yielding their initial ``Schroedinger-like" (i.e.,
ordinary, second-order) linear differential eq. (2.6). Secondly,
they employ a change of variables and make their choice of the two
arbitrary ``input" interaction-characterizing functions $v(x)$ and
$M(x)$ in such a manner that the latter equation gets solvable in
terms of classical orthogonal polynomials (in this step they
successfully recycled the compact notation and approach as proposed
by G\'{e}za L\'{e}vai in 1994 [48]). Thirdly, the usual
``unitarity-of-evolution" (or, if you wish,
``reality-of-potentials-and-masses") constraints are omitted as sort
of obsolete, with an extremely vague citation of refs. [30] - [38]
for the entitlement [which is NOT offered  by any of these purely
heuristic papers since the necessary and appropriate physical ground
of the trick has only been provided later -- see a minimal necessary
explanation as summarized, for example, in my own recent compact
review: M.Z., ``Three-Hilbert-space formulation of Quantum
Mechanics", SIGMA 5 (2009), 001 (arXiv:0901.0700)]. Moreover, in
multiple instants, the all-encompassing text [involving wave
functions constructed in terms of Jacobi (i.e., finite-interval) and
generalized Laguerre and Hermite (i.e., infinite-interval)
polynomials] seems technically incomplete. Indeed, the questions of
boundary conditions are only too often hand-waved away. One can
cite, for example, that ``the wavefunction [(3.8)] becomes a
constant [at a finite boundary point]". One might also feel puzzled
by the unexplained reality-of-spectra constraints (like, e.g.,
(4.10)), or by the mind-boggling validity of the Laguerre-polynomial
solutions over the whole real axis (in spite of the presence of the
centrifugal-like singularity in the origin), etc.

MR2787075 Panahi, H.; Bakhshi, Z. Dirac equation with
position-dependent effective mass and solvable potentials in the
Schrödinger equation. J. Phys. A 44 (2011), no. 17, 175304, 10 pp.
81Qxx